Part B
If Diana spends 25 minutes running at the gym, how many minutes does she spend lifting weights?

The equation ³√x³ = |x| is sometimes true. It is true when x is positive or zero, but not true when x is negative.

The equation ³√x³ = |x| can be classified as "sometimes true.Let's examine the different cases to understand why.

When x is positive or zero (x ≥ 0):

In this case, the cube root of x³ will always be equal to x, as the cube root of a positive number is always positive. Additionally, the absolute value of x is also equal to x when x is positive or zero. Therefore, the equation is true when x is positive or zero.

When x is negative (x < 0):

In this case, the cube root of x³ will be negative because we are taking the cube root of a negative number. However, the absolute value of x will be positive, as it is defined as the magnitude of x without regard to its sign. Therefore, the equation is not true when x is negative.

To summarize, The key factor in determining the validity of the equation is the behavior of the absolute value function and the sign of x. When x is positive or zero, the equation holds true because both sides evaluate to the same value. However, when x is negative, the equation does not hold true because the absolute value of x becomes positive while the cube root of x³ remains negative.

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The box of Cremora is typically rectangular in shape, with six rectangular faces and twelve edges.

Answer:

The answer is C. \(\frac{\sqrt{6} + \sqrt{2} }{4}\)

Step-by-step explanation:

The value of cos(15°) is (√(6) + √(2))/4.

The correct option is C.

The half-angle formula is a trigonometric identity that relates the trigonometric functions of half of an angle to the trigonometric functions of the original angle.

Using half-angle formula for cosine

cos(x/2) = √((1 + cos(x))/2)

In this case, x = 30°, so we have:

cos(15°/2) = √((1 + cos(30°))/2)

cos(15°/2) = √((1 + √(3)/2)/2)

Now, rationalize the denominator:

cos(15°/2) = √((2 + √(3))/4)

cos(15°/2) = √((1/2 + √(3)/4))

Finally, we factor the numerator by multiplying it by (√(2) + √(6))/(√(2) + √(6)):

cos(15°/2) = (√(2) + √(6))/(2√(2))

cos(15°) = (√(2) + sqrt(6))/(2√(2))

By rationalizing the denominator further, we get:

cos(15°) = (√(2) + √(6))/(2√(2))  (√(2)/sqrt(2))

cos(15°) = (√(2)√(2) + √(6)√(2))/(2√(2)√(2))

cos(15°) = (2 + √(12))/(2 x 2)

cos(15°) = (2 + 2√(3))/(4)

cos(15°) = (√(6) + √(2))/4

Therefore, the value of cos(15°) is (√(6) + √(2))/4.

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Answer:

9h=p

9 times the number of hours worked equals the total pay.

The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in (4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in (6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

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Answer:

P(A) = 1/2

Step-by-step explanation:

The question seems incomplete, I assume that we want to find the probability of event A.

Here we have a fair six-sided dice, so each one of the six numbers has exactly the same probability of being rolled.

Such that the possible outcomes of rolling the dice is:

{1, 2, 3, 4, 5, 6}

Now we define event A as rolling an even number.

The possible outcomes such that the event A is true are the even numbers:

{2, 4, 6}

So we have 3 outcomes out of 6.

Then the probability of rolling an even numbers, is just the quotient between the number of outcomes of even numbers (3) and the total number of outcomes (6).

Then:

P(A) = 3/6 = 1/2 = 0.5

Answer:

510.95/5

Step-by-step explanation:

The solution of the equation is ( x - 5 )² +23 = 0.

Completing the square entails writing a quadratic in the form of a squared bracket and, if necessary, adding a constant.

Mathematical symbols can represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping, as well as the order of operations and other features of logical syntax.

Given that the equation is x²-10x = 3. The equation will be solved by completing the square method as below,

x²-10x = 3

x² - 10x - 3 = 0

( x - 5 )² - 3 + 5² = 0

( x - 5 )² - 3 + 25 = 0

( x - 5 )² + 23 = 0

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Answer:

12.4 in

Step-by-step explanation:

I whish i can help :)

Answer:

13.6

Step-by-step explanation:

We can use the pythagorean therom since we know the 2 side leanths and solve for the longest side of the triangle which is the rectangle cut diagonally

11^2+8^2=c^2

121+64=c^2

185=c^2

√185= √c^2

13.6=c

Hope that  helps !

Using algebra, we conclude that the dollar amount of meals Jerome served this weekend is $1150.

Given: The total amount Jerome earned this weekend is $252.50.

           He earned every weekend = $80.

            He earned 15% of the cost of meals as tips by serving them.

To find: The cost of meals served by Jerome in this weekend.

The total amount, $252.50,  is the sum of the tips amount Jerome earned from serving meals and sum of the amount Jerome earned every weekend. To solve this, we must first translate the conditions of the problem, into an algebraic expression with a variable referring to the unknown quantity. This expression is then converted to an equation to find the value of the unknown quantity.

Let x be the cost of meals that Jerome served this weekend.

The equation for the problem statement becomes

\(\$80 + \frac{15}{100} x = \$252.50\\\\\)

Keeping only the x term on the left side of the equation and constant terms on the right side we get

\(\frac{15}{100} x = \$252.50 - \$80\\\\\frac{15}{100} x = \$172.50\\\\\\\)

Multiply both the sides of the equation by 100

\(\frac{15}{100} x \times 100 = \$172.50 \times 100\\\\15x = \$17250\)

Divide both sides of the equation by 15

\(\frac{15x}{15} = \frac{\$17250}{15}\\\\x = \$1150\)

Algebra is a field of mathematics in which letters are substituted for numbers, and an algebraic equation depicts a scale in which what is done on one side of the scale is likewise done on the other side of the scale, with the numbers acting as constants.

An equation is a mathematical statement that two expressions are equal. If it is an algebraic equation, two algebraic expressions has to have the same value  on either side of the equal sign.

A meaningful collection of numbers, variables, and signs (positive or negative) of operations that must make mathematical and logical sense is referred to as an algebraic expression.

Expressions contain any number of algebraic terms. They use signs of operation like addition, subtraction, multiplication, and division and also do not contain an equality sign (=).

Using algebra, we conclude that the dollar amount of meals Jerome served this weekend is $1150.

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Answer:

Answer is B on Edge

F(x)=14-x

Step-by-step explanation:

Answer:

B) f(x) = |14 – x|

Step-by-step explanation:

Edge

Acceptance sampling allows for the inspection of a subset of items from a larger batch, making it suitable for logistics and materials management. It provides a cost-effective way to assess the quality of incoming materials or products, ensuring they meet specified criteria.

In logistics, acceptance sampling helps in verifying the quality of received shipments without the need to inspect every single item. By sampling a representative subset, logistics personnel can quickly assess whether the materials or products meet the required standards. This enables efficient decision-making regarding acceptance, rejection, or further inspection. In materials management, acceptance sampling aids in maintaining quality control throughout the supply chain. By implementing sampling plans at different stages, organizations can identify potential issues early on and take corrective actions,

Reducing the risk of defects or substandard materials reaching the production line. Overall, acceptance sampling enhances efficiency, reduces costs, and facilitates effective logistics and materials management by providing a systematic approach to quality control and inspection.

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Answer: -3,2

Step-by-step explanation:

The options are analyzed as follows:

1: The overline 0.729 means:

This is a non- terminating recurring decimal hence it is rational.

2: The nuumber 0.0195347... is a non terminating and non recurring decimal hence it is irrational.

3. The number -12 is rational since it is an integer.

4.The number 4.565656... is a non terminating recurring decimal hence it is rational.

5. The number given by:

Since square root of 2 is irrational and 3 is rational the product is irrational.

Also the decimal is non terminating non recurring hence it is irratonal.

So the options 2 and 5 are irrational.

The value of x is given as follows:

x = 17.

We obtain the value of x for this problem considering that the sum of the measures of the internal angles of a triangle is of 180º.

The internal angles of the triangle is given as follows:

The sum of the measures of the angles is of 180º, hence the value of x is given as follows:

4x + 3 + x + 7 + 5x = 180

10x + 10 = 180

10x = 170

x = 17.

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Green's theorem can be used to evaluate the line integral along the triangular path from (0, 0) to (2, 0) to (2, 1) to (0, 0) of the function xy dx + y^3 dy.

Green's theorem relates a line integral around a closed curve to a double integral over the region enclosed by the curve. The theorem states that the line integral of a vector field F along a simple closed curve C is equal to the double integral of the curl of F over the region D enclosed by C. In this case, we are given the line integral of the function xy dx + y^3 dy along the triangular path.

To evaluate the line integral using Green's theorem, we first need to find the curl of the vector field associated with the function. The curl of F = (P, Q) is given by ∂Q/∂x - ∂P/∂y, where P and Q are the components of the vector field.

In this case, P = xy and Q = y^3. Taking the partial derivatives, we get ∂Q/∂x = 0 and ∂P/∂y = x. Therefore, the curl of F is 0 - x = -x.

Now, we can evaluate the double integral of the curl of F over the region D enclosed by the triangular path. The region D is a triangle with vertices (0, 0), (2, 0), and (2, 1). By integrating -x over this region, we can find the value of the line integral.

Performing the double integral and simplifying the result will give us the final answer for the line integral along the given path using Green's theorem.

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The outcomes in S are equally likely because each outcome occurs with equal probability.

a) The sample space S with equally likely outcomes is:S = {hh, ht, th, hhh, hht, hth, htt, thh, tht, tth, ttt, ttth, tthh, thth, hthh, httt, tttt}n(S) = 17

b) The sample space S with equally likely outcomes is:S = {hhh, hht, hth, htt, thh, tht, tth, ttt}n(S) = 8The outcomes in S are equally likely because each outcome occurs with equal probability.

c) The event "exactly two heads are tossed" in set notation is {hht, hth, thh}.

d) The event "no tails are tossed" in set notation is {hhh, hht, hth, htt}.

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Answer:

\(122.5\)

Step-by-step explanation:

\(circumference \: = 2\pi \:r\)

\(\pi = 3.14\)

\(r = 19.5\)

Replacing:

\(2 \times 3.14 \times 19.5 = 122.46\)

Therefore, final answer\( = 122.5\)(to the nearest tenth)

The answer is 122.5

In the given question, we have given the radius of the circle and we need to find the circumference of the same.

To need to find the circumference, we must recall this formula

Circumference of circle = \(2\pi r\)

Now, according to the question

Radius = 19.5 cm

Circumference = 2 * \(\pi\) * 19.5

                         = 2 * 3.14 * 19.5       (Taking \(\pi\) = 3.14)

                         = 122.5 cm

Therefore, the circumference of a circle with radius 19.5 cm is 122.5 cm

On rounding off the answer to the nearest tenth, it remains the same.

Hence, the final answer to the question is 122.5 cm.

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Answer:

A

Step-by-step explanation:

The average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

Given,

Benny's arcade has five video game machines

The average time between failures = 34 hours

The maintenance engineer can repair a machine in about = 13 hours

The failure time and repair times are both exponentially distributed

The formula for the mean of an exponential distribution is mean = 1/λ where λ is the rate parameter of the distribution.

In this problem, the rate parameter of both the failure time and repair time is the reciprocal of their respective averages. Therefore,

λ_f = 1/34λ_r = 1/13

Now, let's find the average time from when a machine breaks until it is fixed using the fact that the sum of two independent exponential distributions with rate parameters λ1 and λ2 is itself an exponential distribution with rate parameter λ1+λ2.

So, the rate parameter for the time from when a machine breaks until it is fixed is λ_f+λ_r = 1/34+1/13

= 0.0885 hours⁻¹ (approximately)

Hence, the average time from when a machine breaks until it is fixed is mean = 1/λ= 1/0.0885 ≈ 11.3 hours (approximately).

Therefore, the average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

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Answer:

2x and 4x i guess

Step-by-step explanation:

Answer:

They would be able to make 361 complete packs

The algebraic expression of the statement given as the difference of 27 and 5​ is 27 - 5

The statement is given as:

the difference of 27 and 5​

Difference means minus.

The minus sign is represented as -

This means that the statement given as: the difference of 27 and 5​

Can be represented as

27 minus 5

So, have

27 - 5

Hence, the algebraic expression of the statement given as the difference of 27 and 5​ is 27 - 5

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To find the average temperature for the three hours, we need to sum up the temperatures for each hour and divide by the total number of hours.The average temperature for the three hours is approximately 37.4 degrees Celsius.

Temperature in the first hour: 37.5 degrees Celsius

Temperature in the second hour: 37.5 degrees Celsius

Temperature in the third hour: 37.2 degrees Celsius

To calculate the average temperature:

Average temperature = (Temperature in the first hour + Temperature in the second hour + Temperature in the third hour) / Total number of hours

Average temperature = (37.5 + 37.5 + 37.2) / 3

Calculating the sum:

Average temperature = 112.2 / 3

Dividing by the total number of hours:

Average temperature ≈ 37.4 degrees Celsius

Therefore, the average temperature for the three hours is approximately 37.4 degrees Celsius.

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The normal range of the annual precipitation for Phoenix within one standard deviation of the mean is 26 to 32 inches.

To calculate this, we use the Empirical Rule, which states that in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. In this case, the mean annual precipitation is 29 inches with a standard deviation of 3 inches. Therefore, we can say that approximately 68% of the annual precipitation falls within the range of:

Mean ± 1 x Standard Deviation

= 29 ± 1 x 3

= 26 to 32 inches

This means that for Phoenix, in about 68% of the years, the annual precipitation falls between 26 and 32 inches.

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Answer:

SAS, ASA, SSS, ASA, Yes

Step-by-step explanation: